Question

4. A fort had enough food for 80 soldiers for 60
days. How long would the food last if 20 more
soldiers join after 15 days?
​

Answer 1

Answer:

The food will last for 36 days

Step-by-step explanation:

A fort had enough food for 80 soldiers for 60 days

∴ 80 soldiers each day consume $\frac{1}{60}$ part of food stock

Clearly, each soldier each day consume $\frac{1}{60} . \frac{1}{80}$ part or $\frac{1}{4800}$ part of food stock.

According to the problem, 80 soldiers consumed food for 15 days:

∴ In 15 days, 80 soldiers consumes $\frac{1}{60} . 15 = \frac{1}{4}$ part food of the stock

∴ After 15 days, remaining food stock is $1 - \frac{1}{4} = \frac{3}{4}$  part of food stock

Now additional 20 soldiers joined.

∴ (80 + 20) = 100 Soldiers each day will consume $\frac{1}{4800} . 100$ part of food stock.

$=\frac{1}{48}$ part of food stock.

This means that, for 100 soldiers $\frac{1}{48}$ part of food stock last 1 day

∴ for 100 soldiers $\frac{1}{48} . 48 = 1 whole$ of food stock last 1x48 = 48 days

∴ for 100 soldiers $\frac{3}{4}$ part of food stock last $\frac{3}{4} . 48 = 36$ days

Answer 2

Answer:

⠀Total period = 60 days

After 15 days this period will be = 60 - 15

= 45 days

Number of soldiers in the beginning = 80

Number of soldiers join = 20

New number of soldiers = 80 + 20

= 100 Soldiers.

Number of Soldiers Days

80 45

100 x

More men, the food will last lesser days.

This is an inverse proportion.

80 : 100 : : 45 : x

x = (80*45)/100

x = 36 days

15 days has already gone, so, the food will last for 15 + 36 = 51 days instead of 60 days.⠀⠀⠀⠀⠀⠀⠀⠀

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